A topologically twisted index for three-dimensional supersymmetric theories

By F. Benini, Alberto Zaffaroni. 2015

364 citations recorded by the source corpus.

A bstractWe provide a general formula for the partition function of three-dimensional N=2$$ \mathcal{N}=2 $$ gauge theories placed on S2 ×S1 with a topological twist along S2, which can be interpreted as an index for chiral states of the theories immersed in background magnetic fields. The result is expressed as a sum over magnetic fluxes of the residues of a meromorphic form which is a function of the scalar zero-modes. The partition function depends on a collection of background magnetic fluxes and fugacities for the global symmetries. We illustrate our formula in many examples of 3d Yang-Mills-Chern-Simons theories with matter, including Aharony and Giveon-Kutasov dualities. Finally, our formula generalizes to Ω-backgrounds, as well as two-dimensional theories on S2 and four-dimensional theories on S2 × T2. In particular this provides an alternative way to compute genus-zero A-model topological amplitudes and Gromov-Witten invariants.

Subfields: Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/e156b4f7fed19bda1c13a229c7e4673831db6550

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Citations in the corpus

Supersymmetric partition functions on Riemann surfaces (2016, methodology): “In fact, one can follow almost verbatim the computation in [3], with a few modification that we will discuss here.”
Comments on twisted indices in 3d supersymmetric gauge theories (2016, methodology): “One can similarly study Wilson loop correlation functions and verify that they satisfy the Verlinde algebra [8, 30].”
Black Holes in 4D N=4 Super-Yang-Mills Field Theory (2018, background): “e rst part of the Section is technical, and the uninterested reader could directly jump to Section4.3where the nal result is presented. In the related context of the T2 S2 topologically twisted index [70,12], it was shown in [16] that the basic solution (3.22) leads to the dominant contribution in t”
Fivebranes and 3-manifold homology (2016, methodology): “The contribution for a given h is easily calculated using Jeffrey-Kirwan (JK) contour prescription [34].”
Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes (2018, methodology): “examples. In particular, in [3] the BekensteinHawking entropy of a class of supersymmetric AdS 4 black holes was successfully reproduced from an exact localization computation in the dual ABJM theory [4]. One situation, however, sticks out|the dual eld theoretic understanding of supersymmetric black”
Black hole microstates in AdS4 from supersymmetric localization (2015, methodology): “(A.3) In this Lagrangian we have parametrized the constrained scalar fields La with 20 ~φ = (φ12, φ13, φ14) .”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, background): “For instance, we find that the S3 × S1 partition function [2, 12] can be related to the S2 × T 2 partition function [17, 18] by: ZS3×S1 = 〈F〉S2×T 2 .”
Localization techniques in quantum field theories (2016, background): “(See also [28] for an early discussion.”
Exact microstate counting for dyonic black holes in AdS4 (2016, background): “The Hamiltonian definition of the index is [7] Z(ua,pa) = Tr (−1)F e ∑3 a=1 a Ja e−βH , (14)”
A universal counting of black hole microstates in AdS4 (2017, methodology): “twist that can be applied to three-dimensional N = 2 SCFTs and we argue how for a large class of these twisted theories one can calculate the topologically twisted index of [4] in the planar limit.”
BPS spectra and 3-manifold invariants (2017, background): “along with the symmetry jW ajS ab= jW bjS ba: (3.42) 3.2.2 Topologically twisted index of T[L(p;1)] For group G= SU(2), the topologically twisted index (rened by angular momentum) of T[L(p;1)] reads [56]: I top(q;t) = 1 2 X m2Z Z JK dz 2ˇiz z2(p+2)mq m(1 z2qm)(1 z 2qm) (z2tq1 m;q) 2m 1(z 2tq1+m;q) 2”